In △ABC, D and E are points on the sides AB and AC, respectively, such that DE || BC and DE: BC=6:7. (Area of △ ADE): (Area of trapezium BCED) = ?

ABC is an isosceles triangle such that AB = AC and ∠B = 35°. AD is the median to the base BC. Then ∠BAD is

PQRS is a cyclic quadrilateral. If ∠P is three times of ∠R and ∠S is four times of ∠Q, then the sum of ∠S + ∠R will be:

The centroid of an equilateral triangle PQR is L. If PQ = 6 cm, the length of PL is:

In ∆ABC, the bisector of ∠A intersects side BC at D. If AB = 12 cm, AC = 15 cm and BC= 18 cm, then the length of BD is:

An isosceles triangle ABC is right angled at B.D is a point inside the triangle ABC. P and Q are the feet of the perpendiculars drawn from D on the side AB and AC respectively of ∆ ABC. If AP = a cm, AQ = b cm and ∠BAD = 15°, sin 75°=

The area of the triangle whose vertices are given by the coordinates (1, 2), (-4, -3) and (4, 1) is:

In a circle with centre O, BC is a chord. Points D and A are on the circle, on the opposite side of BC, such that ∠DBC = 28° and BD = DC. What is the measure of ∠BOC?